In similar way, as Sanatan Dharma is based on Vedas and called Vedic Dharma. Vedas are handed down by Rishis who are the Drashta (seer) of Vedic hymns. So, Vedic Dharma laid down by Rishis is called Arsh Dharma.

We find the word "Arsha" being used in the Manu Smriti itself.Its used in the context of declaring the 8 forms of marriage.

Manu Smriti 3.20. Now listen to (the) brief (description of) the
following eight marriage-rites used by the four castes (varna) which
partly secure benefits and partly produce evil both in this life and
after death.

3.21. (They are) the rite of Brahman (Brahma), that of the gods (Daiva), that of the Rishis (Arsha), that of Pragapati (Pragapatya),
that of the Asuras (Asura), that of the Gandharvas (Gandharva), that
of the Rhashasas (Rakshasa), and that of the Pisakas (Paisaka)

Description of Arsha Vivaha is as follows:

3.29. When (the father) gives away his daughter according to the rule, after receiving from the bridegroom, for (the fulfilment of) the
sacred law, a cow and a bull or two pairs, that is named the Arsha
rite.

So,Arsha basically means which is related to the Rishis(Sages) & "Arsha Dharma" is "Dharma which is related to the Rishis" or another way to put it-"Dharma of the Rishis".